When Joseph first starts working at a grocery store, his hourly rate is $\$10$. For each year he works at the grocery store, his hourly rate increases by $\$0.50$. Joseph's hourly rate $R$, in dollars, is a function of $t$, the number of years he works at the grocery store. Write the function's formula. $R=$
Answer: The yearly increase to Joseph's hourly rate is constant, so we're dealing with a linear relationship. We could write the desired formula in slope-intercept form: $R= mt+ b$. In this form, $ m$ gives us the slope of the graph of the function and $ b$ gives us the $y$ -intercept. Our goal is to find the values of $ m$ and $ b$ and substitute them into this formula. We know that for each year Joseph works at the grocery store, his hourly rate increases by $\$0.50$, so the slope $ m$ is ${0.5}$, and our function looks like $R={0.5}t+ b$. We also know that his starting hourly rate is $\$10$, so the $y$ -intercept ${b}$ is ${10}$. Since ${m}={0.5}$ and ${b}={10}$, the desired formula is: $R={0.5}t+{10}$